What about a game where the scum team has no chat and doesn't know who the other ones are?
It wouldn't work. Not without
major change mechanics.
The only main thing that differentiates Mafia from Town is their knowledge of teammates. It's what allows them to stand a chance, despite only having 15-25% of the numbers. Without this knowledge, they're essentially... Town.
Note that 3vs10 Mafia who don't know each other can't figure out whom to lynch. Nor whom to NK. In fact reading wagons becomes meaningless. You can't say "X wouldn't vote for Y" if they're teammates because... X and Y wouldn't know they're teammates if they were. Heck, Mafia can't even win automatically if their numbers become equal to Town because they can't control the lynch, since they don't know whom to lynch. So even when it comes down to 3Mafia vs 1Town it still need to be played out till all Town is dead. "Mafia" is essentially Town B. I guess you could try have a game with both factions starting with same amount of players: Town A vs Town B, where you don't know your teammates and have to eliminate the opposing team. With PRs, including Vig. But it would still be a lot of luck based, since as I mentioned you can't make meaningful wagon analysis.
What could work, and could make for an interesting role (in fact I think such a role might exist) is if
one Mafioso is outside this "perfect knowledge". e.g. in a 17 player game, the Mafia team is made up of 3+1. The three players know each other and can communicate, and the fourth is an outsider. You can then make it either
a) The 3 know who the outsider is. The outsider doesn't know who his teammates are and has to be on the lookout for hints from his teammates.
OR
b) The 3 do not know who the outsider is, while the outsider does know who the three teammates are. In this case it's the three teammates have to be on the lookout for signals from the outsider so they don't accidentally NK him
I think variant (b) is more interesting, but (a) is good too.
Either case, a one-directional knowledge is needed. A case where neither the 3 know who the outsider is, nor vice-versa, gives very little strategy for the outsider. He practically has to rely on luck. Ditto for the 3 on choosing whom to lynch/NK. And again there is no meaningful wagon analysis on the outsider (i.e. if the outsider is killed and flips), since neither he knew the teammates, nor they knew him.
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PS.
I'm surprised no one picked up on
@Ekkologix's fake cop claim.